Question

dilate △abc with a scale factor of 5. enter the new coordinates. a(-1,1) b(4,0) c(1,-3) a=(?,?) b=(?,?) c=(?,?)

Explanation:

Step1: Recall dilation formula

To dilate a point $(x,y)$ with a scale factor $k$ about the origin, the new - point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$. Here $k = 5$.

Step2: Find coordinates of $A'$

For point $A(-1,1)$, with $k = 5$, we have $x=-1$ and $y = 1$. Then $x'=5\times(-1)=-5$ and $y'=5\times1 = 5$. So $A'=(-5,5)$.

Step3: Find coordinates of $B'$

For point $B(4,0)$, with $k = 5$, we have $x = 4$ and $y = 0$. Then $x'=5\times4=20$ and $y'=5\times0 = 0$. So $B'=(20,0)$.

Step4: Find coordinates of $C'$

For point $C(1,-3)$, with $k = 5$, we have $x = 1$ and $y=-3$. Then $x'=5\times1 = 5$ and $y'=5\times(-3)=-15$. So $C'=(5,-15)$.

Answer:

$A'=(-5,5)$
$B'=(20,0)$
$C'=(5,-15)$